Divide the sum of

$\frac{a c x^{2}+(b c+a d) x+b d}{(a x+b)}$

$=\frac{a c x^{2}+b c x+a d x+b d}{(a x+b)}$

$=\frac{c x(a x+b)+d(a x+b)}{(a x+b)}$

$=\frac{(a x+b)(c x+d)}{(a x+b)}$

$=c x+d$